Spawning and Reproductive Success of Hatchery Breeders

Comparison of reproductive success in red drum hatchery adults

SJ O’Leary

2022-06-15

Effective number of breeders

Unequal sex ratios and variance in family sizes among mating combinations (sire X dam) can contribute to the effective number of breeders \(N_{b}\) being reduced compared to the potential number of breeders \(N\) contributing to a given spawning event (i.e. brood fish present in spawning tanks).

The maximum effective number of breeders if all pairs (male x female combinations) contribute equally can be calculated as

(Equation. 1)

\[N_{b(max)} =\frac{4(N_{f}N_{m})}{N_{f} + N_{m}}\]

with \(N_{f}\) and \(N_{m}\) denoting the number of females and males potentially contributing to the spawning event, respectively (???).

Generally, some individuals in a spawning tank will not contribute at all; to determine the reduction in \(N_{b}\) due to some individuals not contributing at all the above equation can be used using the number of male and female broodstock that had progeny assigned to them for \(N_{f}\) and \(N_{m}\).

The effect of variance in family size in reducing the effective number of breeders can be calculated as:

(Equation. 2)

\[N_{b} =\frac{4(N_{bf}N_{bm})}{N_{bf} + N_{bm}}\]

With the effective number of females (\(N_{bf}\)) calculated as

(Equation. 3.1)

\[N_{bf}=\frac{1}{\sum_{k=1}^{n_{f}}q_{k}^2}\]

and the effective number of males (\(N_{bf}\)) calculated as

(Equation. 3.2)

\[N_{bf}=\frac{1}{\sum_{k=1}^{n_{f}}q_{k}^2}\]

with \(N_{f}\) and \(N_{m}\) as the actual number of females and and males contributing to a spawning event, and \(q\) as the proportion of progeny contributed by an adult (Lacy 1989Lacy, Robert C. 1989. “Analysis of founder representation in pedigrees: Founder equivalents and founder genome equivalents.” Zoo Biology 8 (2): 111–23. https://doi.org/10.1002/zoo.1430080203.).

Calculate values of maximum attainable \(N_{b}\) given the number of individuals in tanks contributing to a spawning event, and given the actual number of individuals that did have progeny assigned to them. Determine the effective number of breeders based on variance in family size and calculate the reduction in \(N_{b}\) at each sampling point compared to \(N_{b(max)}\) and the reduction due to the fact that some brood fish do not contribute at all.

Table 1: Comparison of actual and effective number of breeders per spawning event and sample point. Nm and Nf denote the actual number of males and females with progeny assigned to them for a given spawning event/sampling point, N_contrib is the total number of contributing broodfish, Nb(max) is the maximum effective number of breeders if all fish in tanks are successful and contribute equally (Equation 1), Nb(max)’ is the maximum number of effective breeders given the number of males/females that actually had progeny assigned to them, while Nb is the effective number of breeders accounting for variance in family size. Reduct_unsuccessf indicates the reductions in effective number of breeders compared to Nb(max) due to just the fact that some individuals are not successful, while Reduct_variance is the combined effect of both individuals not being successful at all and variance among family size.
E P Nm Nbm Nf Nbf N_tanks F_tanks M_tanks Nb(max) N_contrib Nb(max)’ Nb Reduct_unsuccessf Reduct_variance
YOY-1 T1 5 3.65 3 2.25 10 5 5 10.0 8 7.50 5.56 0.25 0.44
YOY-1 T2 5 4.01 3 2.28 10 5 5 10.0 8 7.50 5.81 0.25 0.42
YOY-1 T3 5 3.71 3 2.49 10 5 5 10.0 8 7.50 5.95 0.25 0.40
YOY-2 T1 7 5.05 5 3.91 20 11 9 19.8 12 11.67 8.82 0.41 0.55
YOY-2 T2 5 3.36 4 3.11 20 11 9 19.8 9 8.89 6.46 0.55 0.67
YOY-2 T3 7 4.27 5 3.41 20 11 9 19.8 12 11.67 7.59 0.41 0.62
YOY-3 T1 4 1.42 4 1.42 15 9 6 14.4 8 8.00 2.84 0.44 0.80
YOY-3 T2 5 2.58 4 2.55 15 9 6 14.4 9 8.89 5.13 0.38 0.64
YOY-3 T3 5 2.65 4 2.63 15 9 6 14.4 9 8.89 5.28 0.38 0.63

Expected contribution per breeder for each spawning event

Spawning event one, two, and three contained progeny from two, four, and three tanks, respectively. Putatively, each tank contains three females and two males, parentage assignment revealed that one adult assumed to be a female is actually male.

For each spawning event, the expected proportion of progeny assigned per breeder was calculated as the proportion of progeny that should be assigned to a breeder if all breeders of the same sex were to contribute to a spawning event with equal success.

Table 2: Number of males and females per spawning event and expected percent of progeny assigned per breeder if all breeders contribute equally.

SPAWNING_EVENT SEX n PERC_OFFSP
YOY-1 F 5 20.00
YOY-1 M 5 20.00
YOY-2 F 11 9.09
YOY-2 M 9 11.11
YOY-3 F 9 11.11
YOY-3 M 6 16.67

Spawning & reproductive success spawning event 1

Spawning success of an adult was calculated as the proportion of progeny assigned to a given breeder at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.

Table 3a: Proportion of progeny assigned per sire for each time point in pond 1

sire T1 T2 T3
ADULT_3160 0.400 0.277 0.258
ADULT_4098 0.218 0.169 0.274
ADULT_4099 0.136 0.193 0.073
ADULT_4154 0.027 0.036 0.048
ADULT_5341 0.218 0.325 0.347

Table 3b: Proportion of progeny assigned per dam for each time point in pond 1

dam T1 T2 T3
ADULT_4114 0.091 0.072 0.129
ADULT_5123 0.564 0.506 0.379
ADULT_9436 0.345 0.422 0.492

Table 3c: Proportion of progeny assigned per pair at stocking.

dam sire n frq
ADULT_4114 ADULT_4098 12 0.10
ADULT_4114 ADULT_5341 4 0.03
ADULT_5123 ADULT_3160 32 0.26
ADULT_5123 ADULT_4099 9 0.07
ADULT_5123 ADULT_4154 6 0.05
ADULT_9436 ADULT_4098 22 0.18
ADULT_9436 ADULT_5341 39 0.31

Adults from two spawning tanks contributed to pond 1.

Table 4: Proprtion of expected progeny assigned per breeder if all breeders are equally successful.

SEX n PERC_OFFSP
F 5 20
M 5 20

Compare the difference in observed vs. expected number of progeny assigned to each breeder.

Figure 1: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).

Figure 1: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).

Compare proportion of progeny assigned to pairs of breeders.

Figure 2: Proportion of progeny assigned to pairs of breeders at each sampling point.

Figure 2: Proportion of progeny assigned to pairs of breeders at each sampling point.

Spawning/reproductive success spawning event 2

Spawning success of an adult was calculated as the proportion of progeny assigned to a given adult at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.

Table 5a: Proportion of progeny assigned per sire for each time point in pond 2.

sire T1 T2 T3
ADULT_3160 0.212 0.077 0.102
ADULT_4098 0.017 NA 0.042
ADULT_4134 0.212 0.385 0.390
ADULT_4136 0.110 0.026 0.144
ADULT_4154 0.161 0.333 0.102
ADULT_5081 0.263 0.179 0.195
ADULT_7514 0.025 NA 0.025

Table 5b: Proportion of progeny assigned per dam for each time point in pond 2.

dam T1 T2 T3
ADULT_5123 0.042 NA 0.068
ADULT_6080 0.203 0.359 0.119
ADULT_7930 0.373 0.205 0.339
ADULT_8155 0.169 0.051 0.085
ADULT_9436 0.212 0.385 0.390

Table 5c: Proportion of progeny assigned per pair at stocking.

dam sire n frq
ADULT_5123 ADULT_4098 5 0.04
ADULT_5123 ADULT_7514 3 0.03
ADULT_6080 ADULT_3160 3 0.03
ADULT_6080 ADULT_4154 11 0.09
ADULT_7930 ADULT_4136 17 0.14
ADULT_7930 ADULT_5081 23 0.19
ADULT_8155 ADULT_3160 9 0.08
ADULT_8155 ADULT_4154 1 0.01
ADULT_9436 ADULT_4134 46 0.39

Adults from four spawning tanks contributed to spawning event 2.

Table 6: Proprtion of expected progeny per breeder if all breeders are equally successful.

SEX n PERC_OFFSP
F 11 9.09
M 9 11.11

Compare the difference in observed vs. expected number of progeny assigned to each breeder.

Figure 3: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).

Figure 3: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).

Compare proportion of progeny assigned to pairs of breeders.

Figure 4: Proportion of progeny assigned to pairs of breeders at each sampling point.

Figure 4: Proportion of progeny assigned to pairs of breeders at each sampling point.

Spawning/reproductive success spawning event 3

Spawning success of an adult was calculated as the proportion of progeny assigned to a given adult at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.

Table 7a: Proportion of progeny assigned per sire for each time point in pond 3.

sire T1 T2 T3
ADULT_3160 NA 0.010 NA
ADULT_4134 0.056 0.152 0.282
ADULT_4136 0.833 0.571 0.526
ADULT_4154 0.037 0.095 0.038
ADULT_5081 NA NA 0.013
ADULT_8311 0.074 0.171 0.141

Table 7b: Proportion of progeny assigned per dam for each time point in pond 3.

dam T1 T2 T3
ADULT_4147 0.056 0.200 0.218
ADULT_6080 0.037 0.105 0.038
ADULT_7930 0.833 0.571 0.538
ADULT_9436 0.074 0.124 0.205

Table 7c: Proportion of progeny per pair at stocking.

dam sire n frq
ADULT_4147 ADULT_4134 13 0.17
ADULT_4147 ADULT_8311 4 0.05
ADULT_6080 ADULT_4154 3 0.04
ADULT_7930 ADULT_4136 41 0.53
ADULT_7930 ADULT_5081 1 0.01
ADULT_9436 ADULT_4134 9 0.12
ADULT_9436 ADULT_8311 7 0.09

Adults from three spawning tanks contributed to spawning event 3.

Table 8: Proprtion of expected progeny per breeder if all breeders are equally successful.

SEX n PERC_OFFSP
F 9 11.11
M 6 16.67

Compare the difference in observed vs. expected number of progeny assigned to each breeder.

Figure 5: Difference of expected and observed proportion of progeny per male and female and total proportion per set of parents per sampling point (breeders that did not have any progeny assigned are not included in figure).

Figure 5: Difference of expected and observed proportion of progeny per male and female and total proportion per set of parents per sampling point (breeders that did not have any progeny assigned are not included in figure).

Compare proportion of progeny assigned to pairs of breeders.

Figure 6: Proportion of progeny assigned to pairs of breeders at each sampling point.

Figure 6: Proportion of progeny assigned to pairs of breeders at each sampling point.

Comparison across spawning events

Comparison expected v realized reproductive success across spawning events

Figure 7: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish

Figure 7: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish

Compare differences by breeder.

Figure 8: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish that successfully participated in more than one spawning event.

Figure 8: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish that successfully participated in more than one spawning event.

Family-wise comparisons

Figure 9: Comparison of proportion of progeny assigned to each family (female x male cross) per spawning event and sampling point.

Figure 9: Comparison of proportion of progeny assigned to each family (female x male cross) per spawning event and sampling point.

Table 9a: Mean family size (as proportion of total progeny) per spawning event.

SPAWNING_EVENT mean sd min max
YOY-1 0.143 0.113 0.024 0.400
YOY-2 0.125 0.119 0.008 0.390
YOY-3 0.150 0.223 0.010 0.833

Table 9b: Number of females a male breeds with (putatively three females and two males present in a spawning tank).

SPAWNING_EVENT mean female partners
YOY-1 1.4
YOY-2 1.3
YOY-3 1.4

Table 9c: Number of males a female breeds with (putatively three females and two males present in a spawning tank).

SPAWNING_EVENT mean male partners
YOY-1 2.3
YOY-2 1.8
YOY-3 1.8

Comparison of reproductive success among breeders

The proportion of progeny assigned to breeders at sampling points T1 and T3 was compared to identify differences in spawning and reproductive success among and within breeders.

Figure 10: Comparison of proportion of progeny released per pond assigned to each breeder. Breeders that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are denoted as filled circles (YOY1 = yellow, YOY2 = turquoise, YOY3 = purple), even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.

Figure 10: Comparison of proportion of progeny released per pond assigned to each breeder. Breeders that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are denoted as filled circles (YOY1 = yellow, YOY2 = turquoise, YOY3 = purple), even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.

Compare across sampling points

Figure 11: Comparison of proportion of progeny assigned to each broodfish per spawning event and sampling point (T1, blue; T2, green, T3, red). Broodstock that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are included, even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.

Figure 11: Comparison of proportion of progeny assigned to each broodfish per spawning event and sampling point (T1, blue; T2, green, T3, red). Broodstock that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are included, even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.

Relationship of age and time spent in hatchery with reproductive success

Estimate approximate age of breeders

Total length and weight was determined for adult red drum caught in the wild and introduced to the hatchery as breeders. Condition at introduction was calculated as the weigt/length ratio (measurements in milimeters and grams). The approximate age at introduction to the hatchery was determined using an age-length regression (Porch, Wilson, and Nieland 2002Porch, Clay E., Charles A. Wilson, and David L. Nieland. 2002. “A new growth model for red drum (sciaenops ocellatus) that accommodates seasonal and ontogenic changes in growth rates.” http://aquaticcommons.org/15199/.) which implements a dampend growth model able to account for a decrease in the growth rate over the lifetime of red drum. Approximate age at spawning was determined as the sum of age at introduction and the time spent in the hatchery.

Determine mean spawning/reproductive success per breeder

Mean reproductive success at sample points T1 and T3 per breeder was determined as the mean proportion of progeny assigned to an adult across spawning events (adults participated in one to three events).

Figure 13: Spawning and reproductive success per breeder/spawning event.

Figure 13: Spawning and reproductive success per breeder/spawning event.

Table 10: Mean spawning and reproductive success per breeder

SAMPLE_ID SEX AGE_INTROD TIME_HATCHERY MEAN_REPROD STD_REPROD MEAN_SPAWN STD_SPAWN N_EVENTS
ADULT_4114 F 4.8 0 0.043 0.074 0.030 0.053 3
ADULT_4147 F 3.9 4 0.073 0.126 0.019 0.032 3
ADULT_4148 F 9.6 3 0.000 0.000 0.000 0.000 2
ADULT_4162 F 31.7 4 0.000 0.000 0.000 0.000 2
ADULT_5123 F 9.6 4 0.224 0.220 0.303 0.369 2
ADULT_6080 F 15.0 0 0.078 0.057 0.120 0.117 2
ADULT_7452 F 22.9 6 0.000 0.000 0.000 0.000 2
ADULT_777 F 12.0 6 0.000 0.000 0.000 0.000 2
ADULT_7930 F 15.0 6 0.438 0.141 0.603 0.325 2
ADULT_8155 F 15.0 4 0.042 0.060 0.084 0.120 2
ADULT_9436 F 20.6 5 0.362 0.145 0.210 0.136 3
ADULT_3160 M 16.8 4 0.120 0.130 0.204 0.200 3
ADULT_4098 M 8.6 3 0.158 0.164 0.118 0.142 2
ADULT_4099 M 12.0 2 0.036 0.052 0.068 0.096 2
ADULT_4134 M 3.2 5 0.336 0.076 0.134 0.110 2
ADULT_4136 M 7.7 5 0.335 0.270 0.472 0.511 2
ADULT_4154 M 3.9 4 0.063 0.034 0.075 0.075 3
ADULT_5081 M 9.6 0 0.104 0.129 0.132 0.186 2
ADULT_5341 M 12.0 5 0.347 0.000 0.218 0.000 1
ADULT_7514 M 18.5 0 0.025 0.000 0.025 0.000 1
ADULT_8311 M 3.2 0 0.070 0.100 0.037 0.052 2

Comparison of reproductive success at T1 and T3 and conditioning parameters

Spearman Rank correlation coefficient is a rank-based (non-parametric) measure of statistical dependence to assess who well relationship of X and Y can be described using a monotone function i.e. Y either strictly increases (or decreases) as X increases even if that relationship is not linear (Y does not increase by same increment for every increment of X).

Figure 15: Reproductive success at sampling point T1 related to conditioning parameters using each spawning event as an independent observation.

Figure 15: Reproductive success at sampling point T1 related to conditioning parameters using each spawning event as an independent observation.

Figure 16: Reproductive success at sampling point T3 related to conditioning parameters using each spawning event as an independent observation.

Figure 16: Reproductive success at sampling point T3 related to conditioning parameters using each spawning event as an independent observation.